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<h1>src/qvmath/qvmatrixalgebra.h</h1><a href="qvmath_2qvmatrixalgebra_8h.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">/*</span>
<a name="l00002"></a>00002 <span class="comment"> *      Copyright (C) 2007, 2008, 2009, 2010, 2011, 2012. PARP Research Group.</span>
<a name="l00003"></a>00003 <span class="comment"> *      &lt;http://perception.inf.um.es&gt;</span>
<a name="l00004"></a>00004 <span class="comment"> *      University of Murcia, Spain.</span>
<a name="l00005"></a>00005 <span class="comment"> *</span>
<a name="l00006"></a>00006 <span class="comment"> *      This file is part of the QVision library.</span>
<a name="l00007"></a>00007 <span class="comment"> *</span>
<a name="l00008"></a>00008 <span class="comment"> *      QVision is free software: you can redistribute it and/or modify</span>
<a name="l00009"></a>00009 <span class="comment"> *      published by the Free Software Foundation, version 3 of the License.</span>
<a name="l00010"></a>00010 <span class="comment"> *</span>
<a name="l00011"></a>00011 <span class="comment"> *      QVision is distributed in the hope that it will be useful,</span>
<a name="l00012"></a>00012 <span class="comment"> *      but WITHOUT ANY WARRANTY; without even the implied warranty of</span>
<a name="l00013"></a>00013 <span class="comment"> *      MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the</span>
<a name="l00014"></a>00014 <span class="comment"> *      GNU Lesser General Public License for more details.</span>
<a name="l00015"></a>00015 <span class="comment"> *</span>
<a name="l00016"></a>00016 <span class="comment"> *      You should have received a copy of the GNU Lesser General Public</span>
<a name="l00017"></a>00017 <span class="comment"> *      License along with QVision. If not, see &lt;http://www.gnu.org/licenses/&gt;.</span>
<a name="l00018"></a>00018 <span class="comment"> */</span>
<a name="l00019"></a>00019 
<a name="l00023"></a>00023 
<a name="l00024"></a>00024 <span class="preprocessor">#ifdef QVMATRIXALGEBRA_AVAILABLE</span>
<a name="l00025"></a>00025 <span class="preprocessor"></span>
<a name="l00026"></a>00026 <span class="preprocessor">#define CHECK_MKL_DSS_ERROR \</span>
<a name="l00027"></a>00027 <span class="preprocessor">    if (error != MKL_DSS_SUCCESS) { \</span>
<a name="l00028"></a>00028 <span class="preprocessor">        std::cout &lt;&lt; &quot;Solver returned error code &quot; &lt;&lt; error &lt;&lt; std::endl; \</span>
<a name="l00029"></a>00029 <span class="preprocessor">        exit(1); \</span>
<a name="l00030"></a>00030 <span class="preprocessor">    }</span>
<a name="l00031"></a>00031 <span class="preprocessor"></span>
<a name="l00032"></a>00032 <span class="preprocessor">#ifndef QMATRIXALGEBRA_H</span>
<a name="l00033"></a>00033 <span class="preprocessor"></span><span class="preprocessor">#define QMATRIXALGEBRA_H</span>
<a name="l00034"></a>00034 <span class="preprocessor"></span>
<a name="l00035"></a>00035 <span class="preprocessor">#include &lt;QV3DPointF&gt;</span>
<a name="l00036"></a>00036 <span class="preprocessor">#include &lt;<a class="code" href="qvmatrix_8h.html" title="File from the QVision library.">qvmath/qvmatrix.h</a>&gt;</span>
<a name="l00037"></a>00037 <span class="preprocessor">#include &lt;QVSparseBlockMatrix&gt;</span>
<a name="l00038"></a>00038 
<a name="l00039"></a>00039 <span class="comment">// Substituted default values.</span>
<a name="l00040"></a>00040 <span class="comment">//      #define DEFAULT_TQVSVD_METHOD                   GSL_THIN_DECOMP_MOD</span>
<a name="l00041"></a>00041 <span class="comment">//      #define DEFAULT_TQVSV_METHOD                    LAPACK_ONLY_DGESVD</span>
<a name="l00042"></a>00042 <span class="comment">//      #define DEFAULT_TQVCHOLESKY_METHOD              GSL_CHOLESKY</span>
<a name="l00043"></a>00043 <span class="comment">//      #define DEFAULT_TQVQR_METHOD                    GSL_HOUSEHOLDER_THIN_QR</span>
<a name="l00044"></a>00044 <span class="comment">//      #define DEFAULT_TQVLU_METHOD                    GSL_LU</span>
<a name="l00045"></a>00045 <span class="comment">//      #define DEFAULT_TQVEIGENDECOMPOSITION_METHOD    GSL_EIGENSYMM</span>
<a name="l00046"></a>00046 <span class="comment">//      #define DEFAULT_TQVEIGENVALUES_METHOD           GSL_EIGENSYMM_ONLY</span>
<a name="l00047"></a>00047 
<a name="l00048"></a>00048 <span class="comment">// Set the default values for the matrix algebra functions to use GSL or LAPACK, whichever is available.</span>
<a name="l00049"></a>00049 <span class="preprocessor">#ifdef LAPACK_AVAILABLE</span>
<a name="l00050"></a>00050 <span class="preprocessor"></span><span class="preprocessor">        #define DEFAULT_TQVSVD_METHOD                   LAPACK_FULL_DGESVD              </span>
<a name="l00051"></a>00051 <span class="preprocessor"></span><span class="preprocessor">        #define DEFAULT_TQVSV_METHOD                    LAPACK_ONLY_DGESVD</span>
<a name="l00052"></a>00052 <span class="preprocessor"></span><span class="preprocessor">        #define DEFAULT_TQVCHOLESKY_METHOD              LAPACK_CHOLESKY_DPOTRF</span>
<a name="l00053"></a>00053 <span class="preprocessor"></span><span class="preprocessor">        #define DEFAULT_TQVQR_METHOD                    LAPACK_FULL_DGEQR2</span>
<a name="l00054"></a>00054 <span class="preprocessor"></span><span class="preprocessor">        #define DEFAULT_TQVLU_METHOD                    LAPACK_DGETRF</span>
<a name="l00055"></a>00055 <span class="preprocessor"></span><span class="preprocessor">        #define DEFAULT_TQVEIGENDECOMPOSITION_METHOD    LAPACK_DSYEV</span>
<a name="l00056"></a>00056 <span class="preprocessor"></span><span class="preprocessor">        #define DEFAULT_TQVEIGENVALUES_METHOD           LAPACK_DSYEV_ONLY</span>
<a name="l00057"></a>00057 <span class="preprocessor"></span><span class="preprocessor">#elif GSL_AVAILABLE</span>
<a name="l00058"></a>00058 <span class="preprocessor"></span><span class="preprocessor">        #define DEFAULT_TQVSVD_METHOD                   GSL_THIN_DECOMP_MOD</span>
<a name="l00059"></a>00059 <span class="preprocessor"></span><span class="preprocessor">        #define DEFAULT_TQVSV_METHOD                    GSL_ONLY_DECOMP</span>
<a name="l00060"></a>00060 <span class="preprocessor"></span><span class="preprocessor">        #define DEFAULT_TQVCHOLESKY_METHOD              GSL_CHOLESKY</span>
<a name="l00061"></a>00061 <span class="preprocessor"></span><span class="preprocessor">        #define DEFAULT_TQVQR_METHOD                    GSL_HOUSEHOLDER_THIN_QR</span>
<a name="l00062"></a>00062 <span class="preprocessor"></span><span class="preprocessor">        #define DEFAULT_TQVLU_METHOD                    GSL_LU</span>
<a name="l00063"></a>00063 <span class="preprocessor"></span><span class="preprocessor">        #define DEFAULT_TQVEIGENDECOMPOSITION_METHOD    GSL_EIGENSYMM</span>
<a name="l00064"></a>00064 <span class="preprocessor"></span><span class="preprocessor">        #define DEFAULT_TQVEIGENVALUES_METHOD           GSL_EIGENSYMM_ONLY</span>
<a name="l00065"></a>00065 <span class="preprocessor"></span><span class="preprocessor">#endif</span>
<a name="l00066"></a>00066 <span class="preprocessor"></span>
<a name="l00067"></a>00067 <span class="preprocessor">#ifdef MKL_AVAILABLE</span>
<a name="l00068"></a>00068 <span class="preprocessor"></span><span class="preprocessor">        #define DEFAULT_TQVSPARSESOLVE_METHOD           QVMKL_DSS</span>
<a name="l00069"></a>00069 <span class="preprocessor"></span><span class="preprocessor">#else</span>
<a name="l00070"></a>00070 <span class="preprocessor"></span><span class="preprocessor">        #define DEFAULT_TQVSPARSESOLVE_METHOD           QV_DENSE</span>
<a name="l00071"></a>00071 <span class="preprocessor"></span><span class="preprocessor">#endif</span>
<a name="l00072"></a>00072 <span class="preprocessor"></span>
<a name="l00075"></a><a class="code" href="group__qvmatrixalgebra.html#gad753ba41cd08df7e8d4173d8c2ac2575">00075</a> <span class="keyword">typedef</span> <span class="keyword">enum</span> {
<a name="l00076"></a><a class="code" href="group__qvmatrixalgebra.html#ggad753ba41cd08df7e8d4173d8c2ac2575a1f02b2cbeb2e75cb9309c6f66ff83e8b">00076</a>     <a class="code" href="group__qvmatrixalgebra.html#ggad753ba41cd08df7e8d4173d8c2ac2575a1f02b2cbeb2e75cb9309c6f66ff83e8b">GSL_THIN_DECOMP_MOD</a>,    
<a name="l00077"></a><a class="code" href="group__qvmatrixalgebra.html#ggad753ba41cd08df7e8d4173d8c2ac2575af5312552984123e0a709bc75f52c008f">00077</a>     <a class="code" href="group__qvmatrixalgebra.html#ggad753ba41cd08df7e8d4173d8c2ac2575af5312552984123e0a709bc75f52c008f">GSL_THIN_DECOMP</a>,        
<a name="l00078"></a><a class="code" href="group__qvmatrixalgebra.html#ggad753ba41cd08df7e8d4173d8c2ac2575a43eb44439df1e8e6797917e721016774">00078</a>     <a class="code" href="group__qvmatrixalgebra.html#ggad753ba41cd08df7e8d4173d8c2ac2575a43eb44439df1e8e6797917e721016774">GSL_THIN_DECOMP_JACOBI</a>, 
<a name="l00079"></a><a class="code" href="group__qvmatrixalgebra.html#ggad753ba41cd08df7e8d4173d8c2ac2575a777aea4370fc3929a00ac3e224508f4c">00079</a>     <a class="code" href="group__qvmatrixalgebra.html#ggad753ba41cd08df7e8d4173d8c2ac2575a777aea4370fc3929a00ac3e224508f4c">LAPACK_FULL_DGESVD</a>,     
<a name="l00080"></a><a class="code" href="group__qvmatrixalgebra.html#ggad753ba41cd08df7e8d4173d8c2ac2575a1686a8461eac2faae7a21c744ac2d05e">00080</a>     <a class="code" href="group__qvmatrixalgebra.html#ggad753ba41cd08df7e8d4173d8c2ac2575a1686a8461eac2faae7a21c744ac2d05e">LAPACK_FULL_DGESDD</a>,     
<a name="l00081"></a><a class="code" href="group__qvmatrixalgebra.html#ggad753ba41cd08df7e8d4173d8c2ac2575ab3bda2bf5279aa36fbc167a0cb434b85">00081</a>     <a class="code" href="group__qvmatrixalgebra.html#ggad753ba41cd08df7e8d4173d8c2ac2575ab3bda2bf5279aa36fbc167a0cb434b85">LAPACK_THIN_DGESVD</a>,     
<a name="l00082"></a><a class="code" href="group__qvmatrixalgebra.html#ggad753ba41cd08df7e8d4173d8c2ac2575a846c64f2016e7d97bda4ceb14b545372">00082</a>     <a class="code" href="group__qvmatrixalgebra.html#ggad753ba41cd08df7e8d4173d8c2ac2575a846c64f2016e7d97bda4ceb14b545372">LAPACK_THIN_DGESDD</a>      
<a name="l00083"></a>00083 } <a class="code" href="group__qvmatrixalgebra.html#gad753ba41cd08df7e8d4173d8c2ac2575" title="Available methods for Singular Value Decomposition (SVD).">TQVSVD_Method</a>;
<a name="l00084"></a>00084 
<a name="l00087"></a><a class="code" href="group__qvmatrixalgebra.html#gae838fb93502416d5876dd38769e3c5a0">00087</a> <span class="keyword">typedef</span> <span class="keyword">enum</span> {
<a name="l00088"></a><a class="code" href="group__qvmatrixalgebra.html#ggae838fb93502416d5876dd38769e3c5a0aec23f378cb62ec5c9647fe24d8b4ab37">00088</a>     <a class="code" href="group__qvmatrixalgebra.html#ggae838fb93502416d5876dd38769e3c5a0aec23f378cb62ec5c9647fe24d8b4ab37">GSL_ONLY_DECOMP_MOD</a>,    
<a name="l00089"></a><a class="code" href="group__qvmatrixalgebra.html#ggae838fb93502416d5876dd38769e3c5a0af7facc299fdba1379bd6ba8acd863125">00089</a>     <a class="code" href="group__qvmatrixalgebra.html#ggae838fb93502416d5876dd38769e3c5a0af7facc299fdba1379bd6ba8acd863125">GSL_ONLY_DECOMP</a>,        
<a name="l00090"></a><a class="code" href="group__qvmatrixalgebra.html#ggae838fb93502416d5876dd38769e3c5a0aae6dd5f0dbab3b0f4d55ad5fb711b6cd">00090</a>     <a class="code" href="group__qvmatrixalgebra.html#ggae838fb93502416d5876dd38769e3c5a0aae6dd5f0dbab3b0f4d55ad5fb711b6cd">GSL_ONLY_DECOMP_JACOBI</a>, 
<a name="l00091"></a><a class="code" href="group__qvmatrixalgebra.html#ggae838fb93502416d5876dd38769e3c5a0a07c014f720d296deab282e63cf84897d">00091</a>     <a class="code" href="group__qvmatrixalgebra.html#ggae838fb93502416d5876dd38769e3c5a0a07c014f720d296deab282e63cf84897d">LAPACK_ONLY_DGESVD</a>,     
<a name="l00092"></a><a class="code" href="group__qvmatrixalgebra.html#ggae838fb93502416d5876dd38769e3c5a0aa99ca829614308fcefd46e2d828dff67">00092</a>     <a class="code" href="group__qvmatrixalgebra.html#ggae838fb93502416d5876dd38769e3c5a0aa99ca829614308fcefd46e2d828dff67">LAPACK_ONLY_DGESDD</a>      
<a name="l00093"></a>00093 } <a class="code" href="group__qvmatrixalgebra.html#gae838fb93502416d5876dd38769e3c5a0" title="Available methods for Singular Values only computation (SV).">TQVSV_Method</a>;
<a name="l00094"></a>00094 
<a name="l00097"></a><a class="code" href="group__qvmatrixalgebra.html#gac52aa1a4772c42c68e53baf5a22e15c8">00097</a> <span class="keyword">typedef</span> <span class="keyword">enum</span> {
<a name="l00098"></a><a class="code" href="group__qvmatrixalgebra.html#ggac52aa1a4772c42c68e53baf5a22e15c8ad805bb0106a0bbf7eea0549f4a5525d1">00098</a>     <a class="code" href="group__qvmatrixalgebra.html#ggac52aa1a4772c42c68e53baf5a22e15c8ad805bb0106a0bbf7eea0549f4a5525d1">GSL_CHOLESKY</a>,           
<a name="l00099"></a><a class="code" href="group__qvmatrixalgebra.html#ggac52aa1a4772c42c68e53baf5a22e15c8a80e13036cfa7096deb292e1b197459bf">00099</a>     <a class="code" href="group__qvmatrixalgebra.html#ggac52aa1a4772c42c68e53baf5a22e15c8a80e13036cfa7096deb292e1b197459bf">LAPACK_CHOLESKY_DPOTRF</a>  
<a name="l00100"></a>00100 } <a class="code" href="group__qvmatrixalgebra.html#gac52aa1a4772c42c68e53baf5a22e15c8" title="Available methods for Cholesky Decomposition.">TQVCholesky_Method</a>;
<a name="l00101"></a>00101 
<a name="l00104"></a><a class="code" href="group__qvmatrixalgebra.html#ga34489f7f981fd3ad10dcd6e287644c21">00104</a> <span class="keyword">typedef</span> <span class="keyword">enum</span> {
<a name="l00105"></a><a class="code" href="group__qvmatrixalgebra.html#gga34489f7f981fd3ad10dcd6e287644c21a17474e8b41843fa89de4b33a88cf3ed4">00105</a>     <a class="code" href="group__qvmatrixalgebra.html#gga34489f7f981fd3ad10dcd6e287644c21a17474e8b41843fa89de4b33a88cf3ed4">GSL_HOUSEHOLDER_THIN_QR</a>,     
<a name="l00106"></a><a class="code" href="group__qvmatrixalgebra.html#gga34489f7f981fd3ad10dcd6e287644c21a052f682a71e7b5e52ae3767b8ccf1532">00106</a>     <a class="code" href="group__qvmatrixalgebra.html#gga34489f7f981fd3ad10dcd6e287644c21a052f682a71e7b5e52ae3767b8ccf1532">GSL_HOUSEHOLDER_FULL_QR</a>,     
<a name="l00107"></a><a class="code" href="group__qvmatrixalgebra.html#gga34489f7f981fd3ad10dcd6e287644c21a4102acc0d67031755466ca0d736b3dd8">00107</a>     <a class="code" href="group__qvmatrixalgebra.html#gga34489f7f981fd3ad10dcd6e287644c21a4102acc0d67031755466ca0d736b3dd8">LAPACK_THIN_DGEQR2</a>,           
<a name="l00108"></a><a class="code" href="group__qvmatrixalgebra.html#gga34489f7f981fd3ad10dcd6e287644c21a5c91dd50e5272c56c5d9a1545ae74919">00108</a>     <a class="code" href="group__qvmatrixalgebra.html#gga34489f7f981fd3ad10dcd6e287644c21a5c91dd50e5272c56c5d9a1545ae74919">LAPACK_FULL_DGEQR2</a>           
<a name="l00109"></a>00109 } <a class="code" href="group__qvmatrixalgebra.html#ga34489f7f981fd3ad10dcd6e287644c21" title="Available methods for QR Decomposition.">TQVQR_Method</a>;
<a name="l00110"></a>00110 
<a name="l00113"></a><a class="code" href="group__qvmatrixalgebra.html#ga3b29cddbb2d5f75b1278f8a6d4abd736">00113</a> <span class="keyword">typedef</span> <span class="keyword">enum</span> {
<a name="l00114"></a><a class="code" href="group__qvmatrixalgebra.html#gga3b29cddbb2d5f75b1278f8a6d4abd736ac377c182c3ec3cc88190908e82e05aef">00114</a>     <a class="code" href="group__qvmatrixalgebra.html#gga3b29cddbb2d5f75b1278f8a6d4abd736ac377c182c3ec3cc88190908e82e05aef">GSL_LU</a>,                 
<a name="l00115"></a><a class="code" href="group__qvmatrixalgebra.html#gga3b29cddbb2d5f75b1278f8a6d4abd736a6ced16c7e295a05f04ae431e76530e43">00115</a>     <a class="code" href="group__qvmatrixalgebra.html#gga3b29cddbb2d5f75b1278f8a6d4abd736a6ced16c7e295a05f04ae431e76530e43">LAPACK_DGETRF</a>           
<a name="l00116"></a>00116 } <a class="code" href="group__qvmatrixalgebra.html#ga3b29cddbb2d5f75b1278f8a6d4abd736" title="Available methods for LU Decomposition.">TQVLU_Method</a>;
<a name="l00117"></a>00117 
<a name="l00120"></a><a class="code" href="group__qvmatrixalgebra.html#gae21e0895ad3ca32f8fdc58b4bf22bec8">00120</a> <span class="keyword">typedef</span> <span class="keyword">enum</span> {
<a name="l00121"></a><a class="code" href="group__qvmatrixalgebra.html#ggae21e0895ad3ca32f8fdc58b4bf22bec8a26b778a18b5ed84f1c9dea5d8419981e">00121</a>     <a class="code" href="group__qvmatrixalgebra.html#ggae21e0895ad3ca32f8fdc58b4bf22bec8a26b778a18b5ed84f1c9dea5d8419981e">GSL_EIGENSYMM</a>,         
<a name="l00122"></a><a class="code" href="group__qvmatrixalgebra.html#ggae21e0895ad3ca32f8fdc58b4bf22bec8a7f4f96ab3bd135f5842b0d25bb5d86a1">00122</a>     <a class="code" href="group__qvmatrixalgebra.html#ggae21e0895ad3ca32f8fdc58b4bf22bec8a7f4f96ab3bd135f5842b0d25bb5d86a1">LAPACK_DSYEV</a>           
<a name="l00123"></a>00123 } <a class="code" href="group__qvmatrixalgebra.html#gae21e0895ad3ca32f8fdc58b4bf22bec8" title="Available methods for EigenDecomposition.">TQVEigenDecomposition_Method</a>;
<a name="l00124"></a>00124 
<a name="l00127"></a><a class="code" href="group__qvmatrixalgebra.html#ga4d0b532a36bb590714b98f651a87f9d2">00127</a> <span class="keyword">typedef</span> <span class="keyword">enum</span> {
<a name="l00128"></a><a class="code" href="group__qvmatrixalgebra.html#gga4d0b532a36bb590714b98f651a87f9d2a6deda0800fef3c39404fa629cc5d00b9">00128</a>     <a class="code" href="group__qvmatrixalgebra.html#gga4d0b532a36bb590714b98f651a87f9d2a6deda0800fef3c39404fa629cc5d00b9">GSL_EIGENSYMM_ONLY</a>,    
<a name="l00129"></a><a class="code" href="group__qvmatrixalgebra.html#gga4d0b532a36bb590714b98f651a87f9d2a135e946a582e39b85260fa48d418ed9e">00129</a>     <a class="code" href="group__qvmatrixalgebra.html#gga4d0b532a36bb590714b98f651a87f9d2a135e946a582e39b85260fa48d418ed9e">LAPACK_DSYEV_ONLY</a>     
<a name="l00130"></a>00130 } <a class="code" href="group__qvmatrixalgebra.html#ga4d0b532a36bb590714b98f651a87f9d2" title="Available methods for EigenValues only computation.">TQVEigenValues_Method</a>;
<a name="l00131"></a>00131 
<a name="l00134"></a><a class="code" href="group__qvmatrixalgebra.html#gaacdaea1a26a36293bfb60ca30909ba42">00134</a> <span class="keyword">typedef</span> <span class="keyword">enum</span> {
<a name="l00136"></a><a class="code" href="group__qvmatrixalgebra.html#ggaacdaea1a26a36293bfb60ca30909ba42a1a4b4a69b2ed71568ebe6c71ed7672cd">00136</a>     <a class="code" href="group__qvmatrixalgebra.html#ggaacdaea1a26a36293bfb60ca30909ba42a1a4b4a69b2ed71568ebe6c71ed7672cd" title="Intel MKL direct sparse solver.">QVMKL_DSS</a> = 0,
<a name="l00138"></a><a class="code" href="group__qvmatrixalgebra.html#ggaacdaea1a26a36293bfb60ca30909ba42a4e5ab535616a47622854edcf1d96684f">00138</a>     <a class="code" href="group__qvmatrixalgebra.html#ggaacdaea1a26a36293bfb60ca30909ba42a4e5ab535616a47622854edcf1d96684f" title="Intel MKL iterative sparse solver.">QVMKL_ISS</a> = 1,
<a name="l00140"></a><a class="code" href="group__qvmatrixalgebra.html#ggaacdaea1a26a36293bfb60ca30909ba42a46209f9833cca62b5a9227d173c6d9a5">00140</a>     <a class="code" href="group__qvmatrixalgebra.html#ggaacdaea1a26a36293bfb60ca30909ba42a46209f9833cca62b5a9227d173c6d9a5" title="CHOLMOD direct sparse solver.">QVCHOLMOD_DSS</a> = 2,
<a name="l00142"></a><a class="code" href="group__qvmatrixalgebra.html#ggaacdaea1a26a36293bfb60ca30909ba42a1cfab50cd282632e71c4a7fe885705b1">00142</a>     <a class="code" href="group__qvmatrixalgebra.html#ggaacdaea1a26a36293bfb60ca30909ba42a1cfab50cd282632e71c4a7fe885705b1" title="Iterative sparse conjugate gradient.">QV_SCG</a> = 3,
<a name="l00144"></a><a class="code" href="group__qvmatrixalgebra.html#ggaacdaea1a26a36293bfb60ca30909ba42a5c07aa6579256ac88d6949c8238c08f4">00144</a>     <a class="code" href="group__qvmatrixalgebra.html#ggaacdaea1a26a36293bfb60ca30909ba42a5c07aa6579256ac88d6949c8238c08f4" title="Block Jacobian preconditioned conjugate gradient.">QV_BJPCG</a> = 4,
<a name="l00146"></a><a class="code" href="group__qvmatrixalgebra.html#ggaacdaea1a26a36293bfb60ca30909ba42a15407dbc0a00f2cf16f73f5b4ec74b67">00146</a>     <a class="code" href="group__qvmatrixalgebra.html#ggaacdaea1a26a36293bfb60ca30909ba42a15407dbc0a00f2cf16f73f5b4ec74b67" title="Direct dense method.">QV_DENSE</a> = 5
<a name="l00147"></a>00147 } <a class="code" href="group__qvmatrixalgebra.html#gaacdaea1a26a36293bfb60ca30909ba42" title="Available methods for sparse linear system solving.">TQVSparseSolve_Method</a>;
<a name="l00148"></a>00148 
<a name="l00149"></a>00149 
<a name="l00174"></a>00174 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#gabe654b66e21aa3d27131c5f65fcc9dfb" title="Obtains the Singular Value Decomposition (SVD) of a rectangular  matrix M.">singularValueDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;U, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;s, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;V, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gad753ba41cd08df7e8d4173d8c2ac2575" title="Available methods for Singular Value Decomposition (SVD).">TQVSVD_Method</a> method = DEFAULT_TQVSVD_METHOD);
<a name="l00175"></a>00175 
<a name="l00176"></a>00176 <span class="preprocessor">#ifndef DOXYGEN_IGNORE_THIS</span>
<a name="l00177"></a>00177 <span class="preprocessor"></span><span class="comment">// This function is deprecated, and should be substituted by the former one.</span>
<a name="l00178"></a>00178 <span class="keywordtype">void</span> SingularValueDecomposition(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;U, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;S, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;V, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gad753ba41cd08df7e8d4173d8c2ac2575" title="Available methods for Singular Value Decomposition (SVD).">TQVSVD_Method</a> method = DEFAULT_TQVSVD_METHOD);
<a name="l00179"></a>00179 <span class="preprocessor">#endif</span>
<a name="l00180"></a>00180 <span class="preprocessor"></span>
<a name="l00198"></a>00198 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#gae7291c840628d8c7f67f90096f470351" title="Solves the linear system  for the unknown matrix , using the previously obtained...">solveFromSingularValueDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;U, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;s, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;V, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;X, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;B);
<a name="l00199"></a>00199 
<a name="l00217"></a>00217 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#gae7291c840628d8c7f67f90096f470351" title="Solves the linear system  for the unknown matrix , using the previously obtained...">solveFromSingularValueDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;U, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;s, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;V, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;b);
<a name="l00218"></a>00218 
<a name="l00243"></a>00243 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#gac5e38c9a7f64b9c7785f4d353c0b9ada" title="Solves the linear system  for the unknown vector , using the singular value decomposition...">solveBySingularValueDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;X, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;B, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gad753ba41cd08df7e8d4173d8c2ac2575" title="Available methods for Singular Value Decomposition (SVD).">TQVSVD_Method</a> method  = DEFAULT_TQVSVD_METHOD);
<a name="l00244"></a>00244 
<a name="l00267"></a>00267 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#gac5e38c9a7f64b9c7785f4d353c0b9ada" title="Solves the linear system  for the unknown vector , using the singular value decomposition...">solveBySingularValueDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;b, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gad753ba41cd08df7e8d4173d8c2ac2575" title="Available methods for Singular Value Decomposition (SVD).">TQVSVD_Method</a> method  = DEFAULT_TQVSVD_METHOD);
<a name="l00268"></a>00268 
<a name="l00293"></a>00293 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#gac5e38c9a7f64b9c7785f4d353c0b9ada" title="Solves the linear system  for the unknown vector , using the singular value decomposition...">solveBySingularValueDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;X, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;B,
<a name="l00294"></a>00294                                        <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;U, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;s, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;V, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gad753ba41cd08df7e8d4173d8c2ac2575" title="Available methods for Singular Value Decomposition (SVD).">TQVSVD_Method</a> method = DEFAULT_TQVSVD_METHOD);
<a name="l00295"></a>00295 
<a name="l00296"></a>00296 
<a name="l00321"></a>00321 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#gac5e38c9a7f64b9c7785f4d353c0b9ada" title="Solves the linear system  for the unknown vector , using the singular value decomposition...">solveBySingularValueDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;b,
<a name="l00322"></a>00322                                        <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;U, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;s, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;V, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gad753ba41cd08df7e8d4173d8c2ac2575" title="Available methods for Singular Value Decomposition (SVD).">TQVSVD_Method</a> method = DEFAULT_TQVSVD_METHOD);
<a name="l00323"></a>00323 
<a name="l00338"></a>00338 <span class="keywordtype">double</span> <a class="code" href="group__qvmatrixalgebra.html#ga78792d4a8a6337b8b92a86a07ede57ac" title="Checks for correctness of the SVD of a matrix.">singularValueDecompositionResidual</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;U, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;s, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;V);
<a name="l00339"></a>00339 
<a name="l00353"></a>00353 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#ga5d6aa6239753252830669883619f5da7" title="Gets the singular values of a matrix.">singularValues</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;s, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gae838fb93502416d5876dd38769e3c5a0" title="Available methods for Singular Values only computation (SV).">TQVSV_Method</a> method = DEFAULT_TQVSV_METHOD);
<a name="l00354"></a>00354 
<a name="l00367"></a>00367 <span class="keywordtype">double</span> <a class="code" href="group__qvmatrixalgebra.html#ga7e4b10036a1a456b58ffcb0ad0e30d52" title="Checks for correctness of the singular values of a matrix.">singularValuesResidual</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;s);
<a name="l00368"></a>00368 
<a name="l00369"></a>00369 
<a name="l00390"></a>00390 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#gab845aa50ce874199ad7676904829b932" title="Obtains the Cholesky decomposition of a symmetric and positive definite matrix.">CholeskyDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;L, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gac52aa1a4772c42c68e53baf5a22e15c8" title="Available methods for Cholesky Decomposition.">TQVCholesky_Method</a> method = DEFAULT_TQVCHOLESKY_METHOD);
<a name="l00391"></a>00391 
<a name="l00405"></a>00405 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#gafc11c4eb4acc7453b7bed072d6bf0a76" title="Solves the linear system  for the unknown matrix , using the previously obtained...">solveFromCholeskyDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;L, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;X, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;B);
<a name="l00406"></a>00406 
<a name="l00419"></a>00419 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#gafc11c4eb4acc7453b7bed072d6bf0a76" title="Solves the linear system  for the unknown matrix , using the previously obtained...">solveFromCholeskyDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;L, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;b);
<a name="l00420"></a>00420 
<a name="l00436"></a>00436 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#ga7afb7ef53aed190e810886e4941bc3de" title="Solves the linear system  for the unknown matrix , using the Cholesky decomposition...">solveByCholeskyDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;X, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;B, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gac52aa1a4772c42c68e53baf5a22e15c8" title="Available methods for Cholesky Decomposition.">TQVCholesky_Method</a> method = DEFAULT_TQVCHOLESKY_METHOD);
<a name="l00437"></a>00437 
<a name="l00451"></a>00451 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#ga7afb7ef53aed190e810886e4941bc3de" title="Solves the linear system  for the unknown matrix , using the Cholesky decomposition...">solveByCholeskyDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;b, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gac52aa1a4772c42c68e53baf5a22e15c8" title="Available methods for Cholesky Decomposition.">TQVCholesky_Method</a> method = DEFAULT_TQVCHOLESKY_METHOD);
<a name="l00452"></a>00452 
<a name="l00469"></a>00469 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#ga7afb7ef53aed190e810886e4941bc3de" title="Solves the linear system  for the unknown matrix , using the Cholesky decomposition...">solveByCholeskyDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;X, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;B, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;L, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gac52aa1a4772c42c68e53baf5a22e15c8" title="Available methods for Cholesky Decomposition.">TQVCholesky_Method</a> method = DEFAULT_TQVCHOLESKY_METHOD);
<a name="l00470"></a>00470 
<a name="l00487"></a>00487 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#ga7afb7ef53aed190e810886e4941bc3de" title="Solves the linear system  for the unknown matrix , using the Cholesky decomposition...">solveByCholeskyDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;b, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;L, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gac52aa1a4772c42c68e53baf5a22e15c8" title="Available methods for Cholesky Decomposition.">TQVCholesky_Method</a> method = DEFAULT_TQVCHOLESKY_METHOD);
<a name="l00488"></a>00488 
<a name="l00501"></a>00501 <span class="keywordtype">double</span> <a class="code" href="group__qvmatrixalgebra.html#gab24bc732bdada660cceccecd98a4a5f2" title="Checks for correctness of the Cholesky decomposition of a matrix.">CholeskyDecompositionResidual</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;L);
<a name="l00502"></a>00502 
<a name="l00503"></a>00503 
<a name="l00527"></a>00527 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#gae5f89f5ce3f124ded687ebdcb4d621bf" title="Obtains the LU decomposition of a rectangular  matrix.">LUDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;P, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;L, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;U, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#ga3b29cddbb2d5f75b1278f8a6d4abd736" title="Available methods for LU Decomposition.">TQVLU_Method</a> method = DEFAULT_TQVLU_METHOD);
<a name="l00528"></a>00528 
<a name="l00546"></a>00546 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#gaa964f05ab494b8a34381d6fa81ce2076" title="Solves the linear system  for the unknown matrix , using the previously obtained...">solveFromLUDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;P, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;L, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;U, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;X, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;B);
<a name="l00547"></a>00547 
<a name="l00562"></a>00562 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#gaa964f05ab494b8a34381d6fa81ce2076" title="Solves the linear system  for the unknown matrix , using the previously obtained...">solveFromLUDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;P, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;L, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;U, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;b);
<a name="l00563"></a>00563 
<a name="l00579"></a>00579 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#ga1e0e534e13e16518cc1c1aa750357a3c" title="Solves the linear system  for the unknown matrix , using the LU decomposition .">solveByLUDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;X, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;B, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#ga3b29cddbb2d5f75b1278f8a6d4abd736" title="Available methods for LU Decomposition.">TQVLU_Method</a> method = DEFAULT_TQVLU_METHOD);
<a name="l00580"></a>00580 
<a name="l00596"></a>00596 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#ga1e0e534e13e16518cc1c1aa750357a3c" title="Solves the linear system  for the unknown matrix , using the LU decomposition .">solveByLUDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;b, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#ga3b29cddbb2d5f75b1278f8a6d4abd736" title="Available methods for LU Decomposition.">TQVLU_Method</a> method = DEFAULT_TQVLU_METHOD);
<a name="l00597"></a>00597 
<a name="l00618"></a>00618 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#ga1e0e534e13e16518cc1c1aa750357a3c" title="Solves the linear system  for the unknown matrix , using the LU decomposition .">solveByLUDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;X, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;B, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;P, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;L, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;U, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#ga3b29cddbb2d5f75b1278f8a6d4abd736" title="Available methods for LU Decomposition.">TQVLU_Method</a> method = DEFAULT_TQVLU_METHOD);
<a name="l00619"></a>00619 
<a name="l00639"></a>00639 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#ga1e0e534e13e16518cc1c1aa750357a3c" title="Solves the linear system  for the unknown matrix , using the LU decomposition .">solveByLUDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;b,<a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;P, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;L, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;U, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#ga3b29cddbb2d5f75b1278f8a6d4abd736" title="Available methods for LU Decomposition.">TQVLU_Method</a> method = DEFAULT_TQVLU_METHOD);
<a name="l00640"></a>00640 
<a name="l00655"></a>00655 <span class="keywordtype">double</span> <a class="code" href="group__qvmatrixalgebra.html#ga88586226df85602c9e139b6d4ee1fbcb" title="Checks for correctness of the LU decomposition of a matrix.">LUDecompositionResidual</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;P, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;L, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;U);
<a name="l00656"></a>00656 
<a name="l00657"></a>00657 
<a name="l00680"></a>00680 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#gadabb7917a1bf7e229a4c7a9b8037b5f0" title="Obtains the QR decomposition of a rectangular  matrix.">QRDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;Q, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;R, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#ga34489f7f981fd3ad10dcd6e287644c21" title="Available methods for QR Decomposition.">TQVQR_Method</a> method = DEFAULT_TQVQR_METHOD);
<a name="l00681"></a>00681 
<a name="l00695"></a>00695 <span class="keywordtype">double</span> <a class="code" href="group__qvmatrixalgebra.html#ga00e06784b460e9b3c4a1377b50b2ccb5" title="Checks for correctness of the QR decomposition of a matrix.">QRDecompositionResidual</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;Q, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;R);
<a name="l00696"></a>00696 
<a name="l00721"></a>00721 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#ga2a46051b1a07328de88e5e73710b7f0b" title="Obtains the QL decomposition of a rectangular  matrix.">QLDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;Q, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;L, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#ga34489f7f981fd3ad10dcd6e287644c21" title="Available methods for QR Decomposition.">TQVQR_Method</a> method = DEFAULT_TQVQR_METHOD);
<a name="l00722"></a>00722 
<a name="l00736"></a>00736 <span class="keywordtype">double</span> <a class="code" href="group__qvmatrixalgebra.html#ga42e745f3d76515e05ab8c16c24e0056a" title="Checks for correctness of the QL decomposition of a matrix.">QLDecompositionResidual</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;Q, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;L);
<a name="l00737"></a>00737 
<a name="l00762"></a>00762 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#gaa825c3d75d892d43c6f20fa3ae909718" title="Obtains the RQ decomposition of a rectangular  matrix.">RQDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;R, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;Q, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#ga34489f7f981fd3ad10dcd6e287644c21" title="Available methods for QR Decomposition.">TQVQR_Method</a> method = DEFAULT_TQVQR_METHOD);
<a name="l00763"></a>00763 
<a name="l00777"></a>00777 <span class="keywordtype">double</span> <a class="code" href="group__qvmatrixalgebra.html#gaa37783c86d91abd724a2eab2cd609ddd" title="Checks for correctness of the RQ decomposition of a matrix.">RQDecompositionResidual</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;R, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;Q);
<a name="l00778"></a>00778 
<a name="l00779"></a>00779 
<a name="l00804"></a>00804 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#gaac2e3437531d9acfec99b6b7ee300392" title="Obtains the LQ decomposition of a rectangular  matrix.">LQDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;L, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;Q, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#ga34489f7f981fd3ad10dcd6e287644c21" title="Available methods for QR Decomposition.">TQVQR_Method</a> method = DEFAULT_TQVQR_METHOD);
<a name="l00805"></a>00805 
<a name="l00819"></a>00819 <span class="keywordtype">double</span> <a class="code" href="group__qvmatrixalgebra.html#gabcf3725f2738f4fb4e823d5a7175ecb9" title="Checks for correctness of the LQ decomposition of a matrix.">LQDecompositionResidual</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;L, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;Q);
<a name="l00820"></a>00820 
<a name="l00837"></a>00837 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#ga4c9f02ada4121317c084f1c7ec09e17c" title="Solves the linear system  for the unknown matrix , using the previously obtained...">solveFromQRDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;Q, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;R, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;X, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;B);
<a name="l00838"></a>00838 
<a name="l00854"></a>00854 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#ga4c9f02ada4121317c084f1c7ec09e17c" title="Solves the linear system  for the unknown matrix , using the previously obtained...">solveFromQRDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;Q, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;R, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;b);
<a name="l00855"></a>00855 
<a name="l00874"></a>00874 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#ga35e4e3e2dd0a5ebbd93f672bf569e4a3" title="Solves the linear system  for the unknown vector , using the QR decomposition of...">solveByQRDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;X, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;B, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#ga34489f7f981fd3ad10dcd6e287644c21" title="Available methods for QR Decomposition.">TQVQR_Method</a> method = DEFAULT_TQVQR_METHOD);
<a name="l00875"></a>00875 
<a name="l00892"></a>00892 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#ga35e4e3e2dd0a5ebbd93f672bf569e4a3" title="Solves the linear system  for the unknown vector , using the QR decomposition of...">solveByQRDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;b, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#ga34489f7f981fd3ad10dcd6e287644c21" title="Available methods for QR Decomposition.">TQVQR_Method</a> method = DEFAULT_TQVQR_METHOD);
<a name="l00893"></a>00893 
<a name="l00914"></a>00914 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#ga35e4e3e2dd0a5ebbd93f672bf569e4a3" title="Solves the linear system  for the unknown vector , using the QR decomposition of...">solveByQRDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;X, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;B,
<a name="l00915"></a>00915                             <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;Q, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;R, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#ga34489f7f981fd3ad10dcd6e287644c21" title="Available methods for QR Decomposition.">TQVQR_Method</a> method = DEFAULT_TQVQR_METHOD);
<a name="l00916"></a>00916 
<a name="l00917"></a>00917 
<a name="l00938"></a>00938 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#ga35e4e3e2dd0a5ebbd93f672bf569e4a3" title="Solves the linear system  for the unknown vector , using the QR decomposition of...">solveByQRDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;b,
<a name="l00939"></a>00939                             <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;Q, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;R, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#ga34489f7f981fd3ad10dcd6e287644c21" title="Available methods for QR Decomposition.">TQVQR_Method</a> method = DEFAULT_TQVQR_METHOD);
<a name="l00940"></a>00940 
<a name="l00964"></a>00964 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#gae95e6a42f2cce467f30a55289a0f9824" title="Obtains the eigen-decomposition of a symmetric matrix.">eigenDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;lambda, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;Q, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gae21e0895ad3ca32f8fdc58b4bf22bec8" title="Available methods for EigenDecomposition.">TQVEigenDecomposition_Method</a> method = DEFAULT_TQVEIGENDECOMPOSITION_METHOD);
<a name="l00965"></a>00965 
<a name="l00979"></a>00979 <span class="keywordtype">double</span> <a class="code" href="group__qvmatrixalgebra.html#ga5ccc97075c8c8d5340dd6b8b2ace3190" title="Checks for correctness of the eigendecomposition of a matrix.">eigenDecompositionResidual</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;lambda, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;Q);
<a name="l00980"></a>00980 
<a name="l00994"></a>00994 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#gabbfe32bf1d0c4def6ecb805bca65d03c" title="Gets the eigenvalues of a matrix.">eigenValues</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;lambda, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#ga4d0b532a36bb590714b98f651a87f9d2" title="Available methods for EigenValues only computation.">TQVEigenValues_Method</a> method = DEFAULT_TQVEIGENVALUES_METHOD);
<a name="l00995"></a>00995 
<a name="l01008"></a>01008 <span class="keywordtype">double</span> <a class="code" href="group__qvmatrixalgebra.html#ga124008527c22895b3dc8b828eb867306" title="Checks for correctness of the eigenvalues of a symmetric matrix.">eigenValuesResidual</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;lambda);
<a name="l01009"></a>01009 
<a name="l01010"></a>01010 
<a name="l01022"></a>01022 <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> <a class="code" href="group__qvmatrixalgebra.html#gadf6472ec782375d465ff1e87b3ae2557" title="Obtains the Moore–Penrose pseudoinverse of a matrix.">pseudoInverse</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gad753ba41cd08df7e8d4173d8c2ac2575" title="Available methods for Singular Value Decomposition (SVD).">TQVSVD_Method</a> method = DEFAULT_TQVSVD_METHOD, <span class="keyword">const</span> <span class="keywordtype">double</span> epsilon = 1.0E-10);
<a name="l01023"></a>01023 
<a name="l01038"></a>01038 <span class="keywordtype">double</span> <a class="code" href="group__qvmatrixalgebra.html#ga18cb128a894fa599a42b85e403049416" title="Obtains the determinant of a square matrix.">determinant</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#ga3b29cddbb2d5f75b1278f8a6d4abd736" title="Available methods for LU Decomposition.">TQVLU_Method</a> method = DEFAULT_TQVLU_METHOD);
<a name="l01039"></a>01039 
<a name="l01056"></a>01056 <span class="keywordtype">void</span> <a class="code" href="group__qvmatrixalgebra.html#gabcefb2cb61ed46e61130f4892308fee4" title="Solves an homogeneous linear system of equations.">solveHomogeneous</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;A, QVector&lt;double&gt; &amp;x, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gad753ba41cd08df7e8d4173d8c2ac2575" title="Available methods for Singular Value Decomposition (SVD).">TQVSVD_Method</a> method = DEFAULT_TQVSVD_METHOD);
<a name="l01057"></a>01057 
<a name="l01073"></a>01073 <span class="keywordtype">double</span> <a class="code" href="group__qvmatrixalgebra.html#ga70717e261a395b8c380c4321dbb12572" title="Returns the residual of the solution to a linear matrix equation.">solveResidual</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;X, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;B);
<a name="l01074"></a>01074 
<a name="l01090"></a>01090 <span class="keywordtype">double</span> <a class="code" href="group__qvmatrixalgebra.html#ga70717e261a395b8c380c4321dbb12572" title="Returns the residual of the solution to a linear matrix equation.">solveResidual</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;b);
<a name="l01091"></a>01091 
<a name="l01092"></a>01092 <span class="preprocessor">#ifndef DOXYGEN_IGNORE_THIS</span>
<a name="l01093"></a>01093 <span class="preprocessor"></span><span class="keyword">extern</span> <span class="keywordtype">int</span> dummy; <span class="comment">// For optional output parameter of next SparseSolve function:</span>
<a name="l01094"></a>01094 <span class="preprocessor">#endif</span>
<a name="l01095"></a>01095 <span class="preprocessor"></span>
<a name="l01123"></a>01123 <span class="keywordtype">double</span> <a class="code" href="group__qvmatrixalgebra.html#gaf7293f186086b4b233cf51046f016158" title="Solves a sparse system of linear equations, taking advantage of sparseness to accelerate...">sparseSolve</a>(<span class="keyword">const</span> <a class="code" href="classQVSparseBlockMatrix.html" title="Implementation of sparse block matrices.">QVSparseBlockMatrix</a> &amp;M, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;b,
<a name="l01124"></a>01124                  <span class="keyword">const</span> <span class="keywordtype">bool</span> isSymmetric = <span class="keyword">false</span>, <span class="keyword">const</span> <span class="keywordtype">bool</span> isPosDefinite = <span class="keyword">false</span>,
<a name="l01125"></a>01125                  <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gaacdaea1a26a36293bfb60ca30909ba42" title="Available methods for sparse linear system solving.">TQVSparseSolve_Method</a> method = DEFAULT_TQVSPARSESOLVE_METHOD, <span class="keyword">const</span> <span class="keywordtype">bool</span> start_from_x = <span class="keyword">false</span>,
<a name="l01126"></a>01126                  <span class="keyword">const</span> <span class="keywordtype">bool</span> iters_or_resid = <span class="keyword">true</span>, <span class="keyword">const</span> <span class="keywordtype">int</span> iters = 0, <span class="keyword">const</span> <span class="keywordtype">double</span> resid = 1.0E-10,
<a name="l01127"></a>01127                  <span class="keywordtype">int</span> &amp;final_iter_count = dummy);
<a name="l01128"></a>01128 
<a name="l01150"></a>01150 <span class="keywordtype">bool</span> <a class="code" href="group__qvmatrixalgebra.html#gabcefb2cb61ed46e61130f4892308fee4" title="Solves an homogeneous linear system of equations.">solveHomogeneous</a>(<span class="keyword">const</span> <a class="code" href="classQVSparseBlockMatrix.html" title="Implementation of sparse block matrices.">QVSparseBlockMatrix</a> &amp;A, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <span class="keywordtype">int</span> maxIterations = 10, <span class="keyword">const</span> <span class="keywordtype">double</span> minRelativeError = 0.0, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gaacdaea1a26a36293bfb60ca30909ba42" title="Available methods for sparse linear system solving.">TQVSparseSolve_Method</a> method=<a class="code" href="group__qvmatrixalgebra.html#ggaacdaea1a26a36293bfb60ca30909ba42a1a4b4a69b2ed71568ebe6c71ed7672cd" title="Intel MKL direct sparse solver.">QVMKL_DSS</a>);
<a name="l01151"></a>01151 
<a name="l01152"></a>01152 <span class="preprocessor">#ifndef DOXYGEN_IGNORE_THIS</span>
<a name="l01153"></a>01153 <span class="preprocessor"></span><span class="keywordtype">void</span> cold_start_mkl_initialization(<span class="keyword">const</span> <span class="keywordtype">int</span> size = 2);
<a name="l01154"></a>01154 
<a name="l01155"></a>01155 <span class="keywordtype">double</span> solveConjugateGradient(<span class="keyword">const</span> <a class="code" href="classQVSparseBlockMatrix.html" title="Implementation of sparse block matrices.">QVSparseBlockMatrix</a> &amp;A, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;b, <span class="keyword">const</span> <span class="keywordtype">int</span> maxIters, <span class="keyword">const</span> <span class="keywordtype">int</span> minIters = 0, <span class="keyword">const</span> <span class="keywordtype">double</span> minAbsoluteError = 0.0);
<a name="l01156"></a>01156 
<a name="l01157"></a>01157 <span class="keywordtype">double</span> <a class="code" href="group__qvmatrixalgebra.html#gaf7293f186086b4b233cf51046f016158" title="Solves a sparse system of linear equations, taking advantage of sparseness to accelerate...">sparseSolve</a>(<span class="keyword">const</span> MKLPardisoSparseFormat &amp;pardisomatrix, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;b,
<a name="l01158"></a>01158                  <span class="keyword">const</span> <span class="keywordtype">bool</span> isSymmetric = <span class="keyword">false</span>, <span class="keyword">const</span> <span class="keywordtype">bool</span> isPosDefinite = <span class="keyword">false</span>,
<a name="l01159"></a>01159                  <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gaacdaea1a26a36293bfb60ca30909ba42" title="Available methods for sparse linear system solving.">TQVSparseSolve_Method</a> method = DEFAULT_TQVSPARSESOLVE_METHOD, <span class="keyword">const</span> <span class="keywordtype">bool</span> start_from_x = <span class="keyword">false</span>,
<a name="l01160"></a>01160                  <span class="keyword">const</span> <span class="keywordtype">bool</span> iters_or_resid = <span class="keyword">true</span>, <span class="keyword">const</span> <span class="keywordtype">int</span> iters = 0, <span class="keyword">const</span> <span class="keywordtype">double</span> resid = 1.0E-10,
<a name="l01161"></a>01161                  <span class="keywordtype">int</span> &amp;final_iter_count = dummy);
<a name="l01162"></a>01162 
<a name="l01163"></a>01163 <span class="comment">// Internal use only. Fast function for homogeneous solving.</span>
<a name="l01164"></a>01164 <span class="preprocessor">#ifdef GSL_AVAILABLE</span>
<a name="l01165"></a>01165 <span class="preprocessor"></span><span class="keywordtype">void</span> solveHomogeneousEig(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;result);
<a name="l01166"></a>01166 <span class="preprocessor">#endif</span>
<a name="l01167"></a>01167 <span class="preprocessor"></span>
<a name="l01169"></a>01169 <span class="keywordtype">void</span> solveLinear(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;A, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;b);
<a name="l01170"></a>01170 
<a name="l01172"></a>01172 <span class="keywordtype">void</span> solveLinear(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;A, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;X, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;B);
<a name="l01173"></a>01173 
<a name="l01175"></a>01175 <span class="keywordtype">void</span> solveOverDetermined(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;A, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;X, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;B);
<a name="l01176"></a>01176 
<a name="l01178"></a>01178 <span class="keywordtype">void</span> solveHomogeneousLinear(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;A, QVector&lt;double&gt; &amp;x);
<a name="l01179"></a>01179 
<a name="l01181"></a>01181 <span class="keywordtype">double</span> homogLineFromMoments(<span class="keywordtype">double</span> x,<span class="keywordtype">double</span> y,<span class="keywordtype">double</span> xx,<span class="keywordtype">double</span> xy,<span class="keywordtype">double</span> yy,<span class="keywordtype">double</span> &amp;a,<span class="keywordtype">double</span> &amp;b,<span class="keywordtype">double</span> &amp;c);
<a name="l01182"></a>01182 
<a name="l01184"></a>01184 <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> <a class="code" href="qvmatrixalgebra_8cpp.html#a2a11aaeedc4d76975389706a8e27defc">regressionLine</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;points);
<a name="l01185"></a>01185 
<a name="l01186"></a>01186 <span class="comment">// Deprecated.</span>
<a name="l01187"></a>01187 <span class="keywordtype">void</span> SingularValueDecomposition(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;U, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;s, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;V, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gad753ba41cd08df7e8d4173d8c2ac2575" title="Available methods for Singular Value Decomposition (SVD).">TQVSVD_Method</a> method = DEFAULT_TQVSVD_METHOD);
<a name="l01188"></a>01188 <span class="keywordtype">void</span> SolveFromSingularValueDecomposition(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;U, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;s, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;V, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;X, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;B);
<a name="l01189"></a>01189 <span class="keywordtype">void</span> SolveFromSingularValueDecomposition(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;U, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;s, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;V, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;b);
<a name="l01190"></a>01190 <span class="keywordtype">void</span> SolveBySingularValueDecomposition(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;X, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;B, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gad753ba41cd08df7e8d4173d8c2ac2575" title="Available methods for Singular Value Decomposition (SVD).">TQVSVD_Method</a> method  = DEFAULT_TQVSVD_METHOD);
<a name="l01191"></a>01191 <span class="keywordtype">void</span> SolveBySingularValueDecomposition(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;b, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gad753ba41cd08df7e8d4173d8c2ac2575" title="Available methods for Singular Value Decomposition (SVD).">TQVSVD_Method</a> method  = DEFAULT_TQVSVD_METHOD);
<a name="l01192"></a>01192 <span class="keywordtype">void</span> SolveBySingularValueDecomposition(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;X, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;B, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;U, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;s, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;V, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gad753ba41cd08df7e8d4173d8c2ac2575" title="Available methods for Singular Value Decomposition (SVD).">TQVSVD_Method</a> method = DEFAULT_TQVSVD_METHOD);
<a name="l01193"></a>01193 <span class="keywordtype">void</span> SolveBySingularValueDecomposition(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;b, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;U, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;s, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;V, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gad753ba41cd08df7e8d4173d8c2ac2575" title="Available methods for Singular Value Decomposition (SVD).">TQVSVD_Method</a> method = DEFAULT_TQVSVD_METHOD);
<a name="l01194"></a>01194 <span class="keywordtype">double</span> SingularValueDecompositionResidual(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;U, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;s, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;V);
<a name="l01195"></a>01195 <span class="keywordtype">void</span> SingularValues(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;s, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gae838fb93502416d5876dd38769e3c5a0" title="Available methods for Singular Values only computation (SV).">TQVSV_Method</a> method = DEFAULT_TQVSV_METHOD);
<a name="l01196"></a>01196 <span class="keywordtype">double</span> SingularValuesResidual(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;s);
<a name="l01197"></a>01197 <span class="keywordtype">void</span> SolveFromCholeskyDecomposition(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;L, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;X, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;B);
<a name="l01198"></a>01198 <span class="keywordtype">void</span> SolveFromCholeskyDecomposition(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;L, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;b);
<a name="l01199"></a>01199 <span class="keywordtype">void</span> SolveByCholeskyDecomposition(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;X, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;B, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gac52aa1a4772c42c68e53baf5a22e15c8" title="Available methods for Cholesky Decomposition.">TQVCholesky_Method</a> method = DEFAULT_TQVCHOLESKY_METHOD);
<a name="l01200"></a>01200 <span class="keywordtype">void</span> SolveByCholeskyDecomposition(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;b, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gac52aa1a4772c42c68e53baf5a22e15c8" title="Available methods for Cholesky Decomposition.">TQVCholesky_Method</a> method = DEFAULT_TQVCHOLESKY_METHOD);
<a name="l01201"></a>01201 <span class="keywordtype">void</span> SolveByCholeskyDecomposition(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;X, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;B, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;L, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gac52aa1a4772c42c68e53baf5a22e15c8" title="Available methods for Cholesky Decomposition.">TQVCholesky_Method</a> method = DEFAULT_TQVCHOLESKY_METHOD);
<a name="l01202"></a>01202 <span class="keywordtype">void</span> SolveByCholeskyDecomposition(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;b, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;L, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gac52aa1a4772c42c68e53baf5a22e15c8" title="Available methods for Cholesky Decomposition.">TQVCholesky_Method</a> method = DEFAULT_TQVCHOLESKY_METHOD);
<a name="l01203"></a>01203 <span class="keywordtype">void</span> SolveFromLUDecomposition(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;P, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;L, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;U, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;X, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;B);
<a name="l01204"></a>01204 <span class="keywordtype">void</span> SolveFromLUDecomposition(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;P, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;L, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;U, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;b);
<a name="l01205"></a>01205 <span class="keywordtype">void</span> SolveByLUDecomposition(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;X, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;B, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#ga3b29cddbb2d5f75b1278f8a6d4abd736" title="Available methods for LU Decomposition.">TQVLU_Method</a> method = DEFAULT_TQVLU_METHOD);
<a name="l01206"></a>01206 <span class="keywordtype">void</span> SolveByLUDecomposition(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;b, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#ga3b29cddbb2d5f75b1278f8a6d4abd736" title="Available methods for LU Decomposition.">TQVLU_Method</a> method = DEFAULT_TQVLU_METHOD);
<a name="l01207"></a>01207 <span class="keywordtype">void</span> SolveByLUDecomposition(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;X, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;B, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;P, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;L, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;U, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#ga3b29cddbb2d5f75b1278f8a6d4abd736" title="Available methods for LU Decomposition.">TQVLU_Method</a> method = DEFAULT_TQVLU_METHOD);
<a name="l01208"></a>01208 <span class="keywordtype">void</span> SolveByLUDecomposition(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;b,<a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;P, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;L, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;U, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#ga3b29cddbb2d5f75b1278f8a6d4abd736" title="Available methods for LU Decomposition.">TQVLU_Method</a> method = DEFAULT_TQVLU_METHOD);
<a name="l01209"></a>01209 <span class="keywordtype">void</span> SolveFromQRDecomposition(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;Q, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;R, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;X, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;B);
<a name="l01210"></a>01210 <span class="keywordtype">void</span> SolveFromQRDecomposition(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;Q, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;R, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;b);
<a name="l01211"></a>01211 <span class="keywordtype">void</span> SolveByQRDecomposition(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;X, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;B, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#ga34489f7f981fd3ad10dcd6e287644c21" title="Available methods for QR Decomposition.">TQVQR_Method</a> method = DEFAULT_TQVQR_METHOD);
<a name="l01212"></a>01212 <span class="keywordtype">void</span> SolveByQRDecomposition(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;b, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#ga34489f7f981fd3ad10dcd6e287644c21" title="Available methods for QR Decomposition.">TQVQR_Method</a> method = DEFAULT_TQVQR_METHOD);
<a name="l01213"></a>01213 <span class="keywordtype">void</span> SolveByQRDecomposition(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;X, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;B, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;Q, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;R, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#ga34489f7f981fd3ad10dcd6e287644c21" title="Available methods for QR Decomposition.">TQVQR_Method</a> method = DEFAULT_TQVQR_METHOD);
<a name="l01214"></a>01214 <span class="keywordtype">void</span> SolveByQRDecomposition(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;b, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;Q, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;R, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#ga34489f7f981fd3ad10dcd6e287644c21" title="Available methods for QR Decomposition.">TQVQR_Method</a> method = DEFAULT_TQVQR_METHOD);
<a name="l01215"></a>01215 <span class="keywordtype">void</span> EigenDecomposition(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;lambda, <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;Q, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gae21e0895ad3ca32f8fdc58b4bf22bec8" title="Available methods for EigenDecomposition.">TQVEigenDecomposition_Method</a> method = DEFAULT_TQVEIGENDECOMPOSITION_METHOD);
<a name="l01216"></a>01216 <span class="keywordtype">double</span> EigenDecompositionResidual(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;lambda, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;Q);
<a name="l01217"></a>01217 <span class="keywordtype">void</span> EigenValues(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;lambda, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#ga4d0b532a36bb590714b98f651a87f9d2" title="Available methods for EigenValues only computation.">TQVEigenValues_Method</a> method = DEFAULT_TQVEIGENVALUES_METHOD);
<a name="l01218"></a>01218 <span class="keywordtype">double</span> EigenValuesResidual(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;lambda);
<a name="l01219"></a>01219 <span class="keywordtype">void</span> SolveHomogeneous(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;A, QVector&lt;double&gt; &amp;x, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gad753ba41cd08df7e8d4173d8c2ac2575" title="Available methods for Singular Value Decomposition (SVD).">TQVSVD_Method</a> method = DEFAULT_TQVSVD_METHOD);
<a name="l01220"></a>01220 <span class="keywordtype">double</span> SolveResidual(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;X, <span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;B);
<a name="l01221"></a>01221 <span class="keywordtype">double</span> SolveResidual(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;M, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;b);
<a name="l01222"></a>01222 <span class="keywordtype">double</span> SparseSolve(<span class="keyword">const</span> <a class="code" href="classQVSparseBlockMatrix.html" title="Implementation of sparse block matrices.">QVSparseBlockMatrix</a> M, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> b,
<a name="l01223"></a>01223                  <span class="keyword">const</span> <span class="keywordtype">bool</span> isSymmetric = <span class="keyword">false</span>, <span class="keyword">const</span> <span class="keywordtype">bool</span> isPosDefinite = <span class="keyword">false</span>,
<a name="l01224"></a>01224                  <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gaacdaea1a26a36293bfb60ca30909ba42" title="Available methods for sparse linear system solving.">TQVSparseSolve_Method</a> method = DEFAULT_TQVSPARSESOLVE_METHOD, <span class="keyword">const</span> <span class="keywordtype">bool</span> start_from_x = <span class="keyword">false</span>,
<a name="l01225"></a>01225                  <span class="keyword">const</span> <span class="keywordtype">bool</span> iters_or_resid = <span class="keyword">true</span>, <span class="keyword">const</span> <span class="keywordtype">int</span> iters = 0, <span class="keyword">const</span> <span class="keywordtype">double</span> resid = 1.0E-10,
<a name="l01226"></a>01226                  <span class="keywordtype">int</span> &amp;final_iter_count = dummy);
<a name="l01227"></a>01227 <span class="keywordtype">void</span> SolveHomogeneous(<span class="keyword">const</span> <a class="code" href="classQVSparseBlockMatrix.html" title="Implementation of sparse block matrices.">QVSparseBlockMatrix</a> &amp;A, <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> &amp;x, <span class="keyword">const</span> <span class="keywordtype">int</span> maxIterations = 10, <span class="keyword">const</span> <span class="keywordtype">double</span> minRelativeError = 0.0, <span class="keyword">const</span> <a class="code" href="group__qvmatrixalgebra.html#gaacdaea1a26a36293bfb60ca30909ba42" title="Available methods for sparse linear system solving.">TQVSparseSolve_Method</a> method=<a class="code" href="group__qvmatrixalgebra.html#ggaacdaea1a26a36293bfb60ca30909ba42a1a4b4a69b2ed71568ebe6c71ed7672cd" title="Intel MKL direct sparse solver.">QVMKL_DSS</a>);
<a name="l01228"></a>01228 <span class="preprocessor">#endif</span>
<a name="l01229"></a>01229 <span class="preprocessor"></span>
<a name="l01230"></a>01230 <span class="preprocessor">#endif // QMATRIXALGEBRA_H</span>
<a name="l01231"></a>01231 <span class="preprocessor"></span>
<a name="l01232"></a>01232 <span class="preprocessor">#endif // QVMATRIXALGEBRA_AVAILABLE</span>
</pre></div></div>
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